Abstract
This paper provides some test cases, called circuits, for the evaluation of Gaussian likelihood maximization algorithms of the cointegrated vector autoregressive model. Both I(1) and I(2) models are considered. The performance of algorithms is compared first in terms of effectiveness, defined as the ability to find the overall maximum. The next step is to compare their efficiency and reliability across experiments. The aim of the paper is to commence a collective learning project by the profession on the actual properties of algorithms for cointegrated vector autoregressive model estimation, in order to improve their quality and, as a consequence, also the reliability of empirical research.
Highlights
Since the late 1980s, cointegrated vector autoregressive models (CVAR) have been extensively used to analyze nonstationary macro-economic data with stochastic trends
This paper proposes a set of test cases to analyze the properties of the numerical algorithms for likelihood maximization of CVAR models
The statistical analysis of CVAR models for data with I(1) stochastic trends was developed in Johansen (1988, 1991)
Summary
Since the late 1980s, cointegrated vector autoregressive models (CVAR) have been extensively used to analyze nonstationary macro-economic data with stochastic trends. Estimation of these models often requires numerical optimization, both for stochastic trends integrated of order 1, I(1), and of order 2, I(2). This paper proposes a set of test cases to analyze the properties of the numerical algorithms for likelihood maximization of CVAR models. This is an attempt to start a collective learning project by the profession about the actual properties of algorithms, in order to improve their quality and, as a consequence, the reliability of empirical research using CVAR models. Gaussian maximum likelihood estimation (MLE) in this model can be performed by Reduced Rank Regression (RRR, see Anderson 1951), which requires the solution of a generalized eigenvalue problem
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